Were they claimed that they managed to solve the prolem?

Are you thought that they will have the chance to visit that place ?

Were they believed that the information was true ?

Was anyone hoped that there would be a significant change in the standards of living ?

Giải thích:

Did => Was, Were

Do => Is, are 

mà những từ như claim, think, believed, hope,... biến đổi thành V2/ed + that clause hoặc to để liên kết vế còn lại 

Chúc bạn học tốt !

.Did they claim that they had managed to solve the problem

=> Were they claimed to have managed to solve the problem?
.Do you think that they will have the chance to visit that place

=> Are they thought to have the chance to visit that place?
.Did they believed that the information was true

=> Was the information believed to be true?
.Did anyone hope that there would be a significant change in the standards of living

=> Was there hoped to be a significant change in the standards of living?